Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
PracticeMATHEMATICAL
PRACTICESThe cost C, in dollars, for pencils is a function of the number n of pencils
purchased. The length L of a pencil, in inches, is a function of the time t, in
seconds, it has been sharpened. Graph the function shown by each table below.
Tell whether the function is linear or nonlinear.See Problem 1.- Pencil Cost 7. Pencil Sharpening
Number of Pencils, n 6 12 18 24 30 T im e (s), f 0 3 6 9 12 15
Cost, C $1 $2 $3 $4 $5 Length (in.), L 7.5 7.5 7.5 7.5 7.4 7.3Graph the function shown by each table. Tell whether the function is
linear or nonlinear.
8.
an on
0 -4
1-3
20
35
VI mP10.
an
0 01 2. F o r t h e d ia g r a m b e lo w , th e ta b le g iv e s th e t o t a l n u m b e r o f
s m a ll t r ia n g le s y i n fig u r e n u m b e r x. W h a t p a t t e r n c a n y o u
use to com plete the table? Represent the relationship using
words, an equation, and a graph.A
Figure 1a | a
Figure 2A A A
aa| aa
Figure 311.
on
00
13
26
39See Problem 2.Total Small
Triangles, y1
(^13) (1, 3)
(^212) (2,12)
(^327) (3, 27)
(^4) « m
(^5) ■■
Each set of ordered pairs represents a function. Write a rule that represents
the function.
See Problem 3.
- (0, 0), (1, 4), (2, 16), (3, 36), (4, 64)
- (1, 2), (2,16), (3, 54), (4, 128), (5, 250)
1 4 - ('■ !)■ t 2 ’ I ) - f 3 ' A ) ' t 4 ' i f ) ' ( 5 ' H )- (0, 0), (1, 0.5), (2, 2), (3, 4.5), (4, 8)
©Apply @17. Writing The rule V = | r r r 3 g i v e s t h e v o l u m e Vof a s p h e r e a s a f u n c t i o n o f i t s
radius r. Id e n tify th e in d e p e n d e n t a nd d e p e n d e n t variables in th is re la tio n sh ip.
E x p la in y o u r r e a s o n in g.- Open-Ended W r it e a r u le f o r a n o n lin e a r f u n c t i o n s u c h t h a t y is n e g a tiv e w h e n
x = 1, p o s it iv e w h e n x = 2, n e g a tiv e w h e n x = 3, p o s it iv e w h e n x = 4, a n d so o n.
250 Chapter 4 An Introduction to Functions